1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Svetradugi [14.3K]
3 years ago
7

Gravel is being dumped from a conveyor belt at a rate of 35 ft3/min, and its coarseness is such that it forms a pile in the shap

e of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 10 ft high? (Round your answer to two decimal places.)
Mathematics
1 answer:
Luda [366]3 years ago
4 0

Answer:

0.45 ft/min

Step-by-step explanation:

Given:-

- The flow rate of the gravel, \frac{dV}{dt} = 35 \frac{ft^3}{min}

- The base diameter ( d ) of cone = x

- The height ( h ) of cone = x

Find:-

How fast is the height of the pile increasing when the pile is 10 ft high?

Solution:-

- The constant flow rate of gravel dumped onto the conveyor belt is given to be 35 ft^3 / min.

- The gravel pile up into a heap of a conical shape such that base diameter ( d ) and the height ( h ) always remain the same. That is these parameter increase at the same rate.

- We develop a function of volume ( V ) of the heap piled up on conveyor belt in a conical shape as follows:

                                V = \frac{\pi }{12}*d^2*h\\\\V = \frac{\pi }{12}*x^3

- Now we know that the volume ( V ) is a function of its base diameter and height ( x ). Where x is an implicit function of time ( t ). We will develop a rate of change expression of the volume of gravel piled as follows Use the chain rule of ordinary derivatives:

                               \frac{dV}{dt} = \frac{dV}{dx}  * \frac{dx}{dt}\\\\\frac{dV}{dt} = \frac{\pi }{4} x^2 * \frac{dx}{dt}\\\\\frac{dx}{dt} = \frac{\frac{dV}{dt}}{\frac{\pi }{4} x^2}

- Determine the rate of change of height ( h ) using the relation developed above when height is 10 ft:

                              h = x\\\\\frac{dh}{dt} = \frac{dx}{dt} = \frac{35 \frac{ft^3}{min} }{\frac{\pi }{4}*10^2 ft^2 }   \\\\\frac{dh}{dt} = \frac{dx}{dt} = 0.45 \frac{ft}{min}

You might be interested in
At the rodeo, 256 hot dogs were sold
Rzqust [24]

Answer:

B. $72

Step-by-step explanation:

$768 / 256 = $3 per hot dog

So $3 • 24 = $72

3 0
3 years ago
Solve for r.
Serhud [2]

If I assume that p is supposed to be r, then:

r = 12.5

or

r = 25/2 is improper or 12 & 1/2 is proper

8 0
3 years ago
What is the solution to 2x + 8 > 10 ?
djyliett [7]
2x + 8 > 10
You first move + 8 to the other side, so you subtract 8
(When you see addition, you perform subtraction)
2x + 8 - 8  > 10 - 8
+ 8 and - 8 cancels out
2x > 2
Now, to isolate x, you should divide both sides by 2
(When you see multiplication, you perform division)
\frac{2x}{2} > \frac{2}{2}
2 and 2 cancels out and we are left with
x > 1
So your final answer will be x > 1
6 0
3 years ago
What is the median of 5, 2, 9, 21, 12, 3
finlep [7]

2, 3,5,12,21

it is 5

this is the answer

7 0
3 years ago
Read 2 more answers
What’s the area of segment (shaded region) PLEASE HELP FAST
Ainat [17]

Answer:

find the area if the sector,then the area of the triangle.After that, Subtract the area of the triangle from the area of the sector

4 0
2 years ago
Other questions:
  • 721 lbs per week into kg per second SHOW WORK PLEASE:)
    8·1 answer
  • Find the savings plan balance after 12 months with apr of 3% and monthly payments of $150
    14·1 answer
  • which one of the following equations describes the line shown below check all that apply (-1,6) (2,-6)
    11·1 answer
  • Which angles are complementary?
    12·2 answers
  • 1 a) A random sample of 25 was drawn from a normal distribution with a standard deviation of 5. The sample mean is 80. Determine
    13·1 answer
  • Jason has 5 boxes and 3 cases of soup cans Each box contains 6 cans and each case contains 36 cans How many cans of soup does Ja
    8·1 answer
  • 24. $5.24 + 23¢ + 2¢ (53)​
    9·1 answer
  • The area of a circle, in terms of <br> π<br> , is 36<br> π<br> m2.<br> Find the value of the radius.
    10·1 answer
  • How can you find a function that has<br> roots?
    5·2 answers
  • Una fracción equivalente a 3/4​
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!